The region of validity of homogeneous nucleation theory

We examine the region of validity of Langerʹs picture of homogeneous nucleation. Our approach is based on a coarse-grained free energy that incorporates the effect of fluctuations with momenta above a scale k. The nucleation rate I=Akexp(−Sk) is exponentially suppressed by the action Sk of the saddle-point configuration that dominates tunnelling. The factor Ak includes a fluctuation determinant around this saddle point. Both Sk and Ak depend on the choice of k, but, for 1/k close to the characteristic length scale of the saddle point, this dependence cancels in the expression for the nucleation rate. For very weak first-order phase transitions or in the vicinity of the spinodal decomposition line, the pre-exponential factor Ak compensates the exponential suppression exp(−Sk). In these regions the standard nucleation picture breaks down. We give an approximate expression for Ak in terms of the saddle-point profile, which can be used for quantitative estimates and practical tests of the validity of homogeneous nucleation theory.